SEOUL, June 13 (Reuters) - South Korean parents, well known for marching their children off to cram schools, have been enrolling their youngsters in safety classes since hundreds of people were killed in a ferry sinking in April.

The ferry, the Sewol, overloaded and travelling too fast on a turn, capsized and sank off the southwest coast on April 16, killing more than 300 people, most of them children and teachers from the same school on a class trip.

The fire department in the capital, Seoul, said bookings for its safety classes had risen 20 percent since the ferry accident. Sales of life jackets had more than doubled, said top discount retailer E-Mart.

"The Sewol was different. Too many kids died and it struck the hearts of many parents," Lee Eun-jung, a 46-year-old mother, said this week as she picked up her three girls coming out of a class on how to stay safe in fires and earthquakes.

"We weren't affected by the accident but I've been heartbroken ever since," she said.

The Sewol was on a routine journey from Incheon on the mainland to the southern holiday island of Jeju when it went down.

One of Lee's daughters happened to be flying to Jeju on a school trip on the same day, making the disaster that much more poignant for their family.

"This won't be forgotten. People will change a lot because of this," Lee said.

South Korea, Asia's fourth-largest economy, has developed into a vibrant and technically advanced democracy, but it faces criticism that regulatory controls and safety standards have not kept pace.

It is not just the ferry disaster that has alarmed parents.

There have been a string of accident in recent weeks including a fire at a hospital for the elderly on May 28 that killed 21 people.

Two days earlier, a fire at a shopping mall killed eight people. Nearly 200 people were injured in two subway accidents in Seoul since early May.

'ENORMOUS SHOCK'

Investigators say confusion and chaos reigned on the Sewol as it began to list.

Many of the children died obeying orders to wait in their cabins while many of the crew members abandoned ship. Fifteen surviving crew members are facing trial, including the captain and three others who face homicide charges.

The disaster has highlighted a culture of cosy personal ties that frequently blur the lines between businesses and those in government who regulate them often at the expense of safety.

President Park Geun-hye, whose government has been sharply criticized for a slow and ineffective rescue effort, has vowed to reform bureaucracy and safety oversight.

The prime minister resigned over the government's response.

Experts say South Korea has learned a harsh lesson from the disaster and this time, the tragedy might just be enough to change deep-rooted apathy over safety.

"The shock has been enormous," said Shim Jun-seop, a public service professor at Chung-Ang University in Seoul.

"I think it will change many things in safety and risk management including disasters."

Now even children realise there is much to do to minimise risks.

"I felt something was missing because I haven't learned how to swim," said 11-year-old Shin Ji-won, coming out of an coaching session on emergency drills.

Shin said she would have been in big trouble if she had been on the Sewol: "I would have panicked ... I don't even want to think about it." (Additional reporting by Kahyun Yang; Editing by Robert Birsel)